Version 5.0 The LEDA User Manual

arithmetic demand for each function below. If the arithmetic incurs rounding error, the
computation may fail in two ways: give a wrong answer or run forever.
12.1 Basic Graph Algorithms ( basic graph alg )
bool
TOPSORT(const graph& G, node array& ord)
TOPSORT takes as argument a directed graph G(V, E). It sorts G topologically
(if G is acyclic) by computing for every node v ∈ V an integer
ord[v] such that 1 ≤ ord[v] ≤ |V | and ord[v] < ord[w] for all edges
(v, w) ∈ E. TOPSORT returns true if G is acyclic and false otherwise.
The algorithm ([50]) has running time O(|V | + |E|).
bool TOPSORT(const graph& G, list& L)
a variant of TOPSORT that computes a list L of nodes in topological
order (if G is acyclic). It returns true if G is acyclic and false otherwise.
list DFS(const graph& G, node s, node array& reached)
DFS takes as argument a directed graph G(V, E), a node s of G and a
node array reached of boolean values. It performs a depth first search
starting at s visiting all reachable nodes v with reached[v] = false. For
every visited node v reached[v] is changed to true. DFS returns the list
of all reached nodes. The algorithm ([85]) has running time O(|V | + |E|).
list DFS NUM(const graph& G, node array& dfsnum,
node array& compnum)
DFS NUM takes as argument a directed graph G(V, E). It performs a
depth first search of G numbering the nodes of G in two different ways.
dfsnum is a numbering with respect to the calling time and compnum
a numbering with respect to the completion time of the recursive calls.
DFS NUM returns a depth first search forest of G (list of tree edges).
The algorithm ([85]) has running time O(|V | + |E|).
list BFS(const graph& G, node s, node array& dist)
BFS takes as argument a directed graph G(V, E),a node s of G and a
node array dist of integers. It performs a breadth first search starting at
s visiting all nodes v with dist[v] = −1 reachable from s. The dist value
of every visited node is replaced by its distance to s. BFS returns the list
of all visited nodes. The algorithm ([58]) has running time O(|V | + |E|).